A135704 a(n) = 7*n^2 + 4*n + 1.

4, 1, 12, 37, 76, 129, 196, 277, 372, 481, 604, 741, 892, 1057, 1236, 1429, 1636, 1857, 2092, 2341, 2604, 2881, 3172, 3477, 3796, 4129, 4476, 4837, 5212, 5601, 6004, 6421, 6852, 7297, 7756, 8229, 8716, 9217, 9732, 10261, 10804, 11361, 11932

Offset

-1,1

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

L. Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = a(n-1) + 14*n - 3, with a(-1)=4. - Vincenzo Librandi, Nov 18 2010

From G. C. Greubel, Oct 29 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (4 - 11*x + 21*x^2)/(x * (1 - x)^3).

E.g.f.: 4/x + (1 + 11*x + 7*x^2)*exp(x). (End)

Mathematica

Table[7n^2+4n+1, {n, -1, 50}]  (* Harvey P. Dale, Mar 26 2011 *)
LinearRecurrence[{3, -3, 1}, {4, 1, 12}, 25] (* G. C. Greubel, Oct 29 2016 *)

Prog

(PARI) a(n)=7*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

This is simply A005892 with offset -1.

Sequence in context: A019238 A299523 A157404 * A373394 A002564 A287640

Adjacent sequences: A135701 A135702 A135703 * A135705 A135706 A135707

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 04 2008

Status

approved